In this work, we consider the stochastic fractional-space Kuramoto–Sivashinsky equation using conformable derivative. The Riccati method is used to get analytical solutions space-fractional equation. Because has never been examined with and multiplicative noise at same time, generalize some previous results. Moreover, display how influences on stability of obtained

We present a novel control methodology to control the roughening processes of semilinear parabolic stochastic partial differential equations in one dimension, which we exemplify with the stochastic Kuramoto-Sivashinsky equation. The original equation is split into a linear stochastic and a nonlinear deterministic equation so that we can apply linear feedback control methods. Our control strateg...

We report numerical simulations of one-dimensional cellular solutions of the stabilized Kuramoto-Sivashinsky equation. This equation offers a range of generic behavior in pattern-forming instabilities of moving interfaces, such as a host of secondary instabilities or transition toward disorder. We compare some of these collective behaviors to those observed in experiments. In particular, destab...

In this paper, we use a methodology that was recently proposed by Antoniades and Christofides to compute the optimal actuator/sensor locations for the stabilization, via nonlinear static output feedback control, of the zero solution of the Kuramoto–Sivashinsky equation (KSE) for values of the instability parameter for which this solution is unstable. The theoretical results are illustrated thro...

We study the step meandering instability on a surface characterized by the alternation of terraces with different properties, as in the case of Si(001). The interplay between diffusion anisotropy and step stiffness induces a finite wavelength instability corresponding to a meandering mode. The instability sets in beyond a threshold value which depends on the relative magnitudes of the destabili...

We consider a system formed by an infinite viscous liquid layer with a constant horizontal temperature gradient, and a basic nonlinear bulk velocity profile. In the limit of long-wavelength and large nondimensional surface tension, we show that hydrothermal surface-wave instabilities may give rise to disturbances governed by the Kuramoto-Sivashinsky equation. A possible connection to hot-wire e...